\newproblem{lay:6_6_9}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 6.6.9}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	A certain experiment produces the data (1,7.9), (2,5.4) and (3,-0.9). Describe the model that produces a least-squares fit of these points by a function
	of the form
	\begin{center}
		$y=A\cos(x)+B\sin(x)$
	\end{center}
}{
   % Solution
	For each one of the data points we have a linear equation
	\begin{center}
		$7.9=A\cos(1)+B\sin(1)$ \\
		$5.4=A\cos(2)+B\sin(2)$ \\
		$-0.9=A\cos(3)+B\sin(3)$ \\
	\end{center}
	This can be rewritten in matrix form as
	\begin{center}
		$\begin{pmatrix} \cos(1) & \sin(1) \\ \cos(2) & \sin(2) \\ \cos(3) & \sin(3) \end{pmatrix} \begin{pmatrix} A\\B \end{pmatrix}=\begin{pmatrix}7.9\\5.4\\-0.9 \end{pmatrix}$
	\end{center}
	so we are back to the framework of least-squares fittings and we can solve for $A$ and $B$ by using the normal equations of the problem.
}
\useproblem{lay:6_6_9}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}

